Energy & Momentum Flashcards
Equation: Work done on an object by a constant force
W = F * d * cos(ø)
SI Unit = Joule = Newton * meter
Note: F = magnitude of force, d = mag of displacement, and ø = angle between force and displacement
Only the component of the force ________ the displacement is used to define work
along the displacement
In the absence of non-conservative forces (i.e. gravity), the work is independent of the _______.
Path taken
i.e. block lifted vertically or pushed up an inclined plane depends only on net vertical displacement
Equation: Kinetic Energy
KE = 1/2 * m * v^2
SI Unit = Joule (J)
Equation: Net Work done by ∆KE
W(net) = ∆KE = KE(f) - KE(o) = 1/2mv(f)^2 - 1/2mv(o)^2
Explains the amount of energy that an object of mass m has by virtue of its position relative to the surface of the earth. Position is measured by the height (h) of the object relative to an arbitrary zero level
work-energy theorem
Equation: Work-Energy Theorem
PE = mgh
Note: h = height above the earth
SI Unit = Joule (J)
Equation: Gravitational Potential Energy
PE = mgh
Defined as a change in the KE of a system
Work
SI Unit = Joule
Equation: Conservation of Energy
KE(i) + PE(i) = KE(f) + PE(f)
In the absence of forces like friction, mechanical energy is _______.
Conserved.
If the kinetic energy of an object increases by a certain amount, its potential energy ________.
Decreases by the same amount
the rate at which work is done
= work / time it took to perform the work
Power
Equation: Power
Power = Work / Time = W / t
SI Unit = Joule/second = Watt (W)
product of an object’s mass times its velocity
vector quantity that points in the same direction as velocity
conserved in the absence of an outside nonconservative force
momentum (p)
SI Unit = kg * m / sec
Equation : Momentum
p = m * v
SI Unit = kg * m / sec
a collision in which the total kinetic energy of the system after the collision is equal to the total kinetic energy before the collision
elastic collision
Equation: Conservation of momentum
Applied to elastic collisions
(m1 * v1i) + (m2 * v2i) = (m1 * v1f) + (m2 * v2f)
Collision in which the kinetic energy of the system is not conserved
collision in which the total KE of the system is not the same before and after the collision
inelastic collision
collision in which objects collide and stick together
completely inelastic collision
Equation: Conservation of Momentum for Completely Inelastic collisions
m1 * v1(i) + m2 * v2(i) = (m1 + m2) * v(f)
In collision equations, make sure to account for the ________ of each momentum, which is a vector quantity.
direction
*If objects are moving toward each other, one velocity vector will be positive and one will be negative
springs exhibit ______ behavior
elastic
Equation: Hooke’s Law
F(restoring) = -k * x
SI Unit: N / m
Note: -k = spring constant (proportionality constant)
x = displacement of the spring from its unstrained length
described by Hooke’s law
always points in a direction opposite to the displacement of the spring
restoring force
spring constant / proportionality constant
describes stiffness of the spring
higher the value of this, the harder it is to stretch or compress the spring
k (-k in Hooke’s law equation)
maximum displacement from equilibrium
amplitude
for any object in simple harmonic motion, the time required to complete one cycle is called the ______
Period (T)
number of cycles of motion per second
inverse of period (T)
measured in Hertz = 1 / sec
Frequency (f)
Equation: Frequency
Frequency (f) = 1 / T
SI Unit: 1 / sec
frequency at which object of mass m vibrates on a spring
expressed in radians per second
angular frequency (omega)
Equation: Angular Frequency
angular frequency (omega) = 2 * π / T = 2 * π * f = √(k/m) SI unit = Radians / second
energy that a spring has because of being stretched or compressed
elastic potential energy (PE elastic)
Equation: Elastic Potential Energy: PE (elastic)
PE(elastic) = 1/2 * k * x^2
SI Unit = Joule
at max displacement from equilibrium, the PE of the spring is at a ________ and the KE is _________
PE = maximum KE = 0
total mechanical energy is conserved when nonconservative forces do no work
conservation of mechanical energy
Equation: Conservation of Mechanical Energy
E(f) = E(i)
Equation: Total Mechanical Energy
E(total) = 1/2mv^2 + mgh + 1/2kx^2
SI Unit = Joule
Equation: Angular Freqency
Angular Frequency (omega) = 2πf = √(g/L) Note: g = 10 m/s^2 and L = length (m)
The PE of a mass at its equilibrium position =
0
